This study investigates the longitudinal velocity profiles in steady and unsteady non-uniform open channel flows by analyzing the data available in the literature. It was found that for steady/unsteady flow in the Log law is applicable only in the inner region where y/hg<0.2 when compared with the measured longitudinal velocity. However, in the main flow, the measured vlocity deviates significantly from Log law's prediction. The detail assessment shows that the deviation is negative when a flow is accelerating, and positive when declelerating. The reason for this deviation is explained by linking these deviations with the presence of wall-normal velocity. A new equation was developed to express the velocity in non-uniform flow which is valid for uniform flows (Log law) and accelerating
and decelerating steady/unsteady flows, in which Log law, Cole’s Wake law and Dip law
have been combined together to reflect the influence of acceleration on the velocity profile.
This modification has been verified with experimental data sets available in the literature,
and a reasonable agreement between the measured and predicted mean velocity profile is